Question

1. find ( mangle cdb ).

Explanation:

Step1: Find the length of \(BD\)

In right - triangle \(ABD\), \(\sin A=\frac{BD}{AB}\). Given \(AB = 18\) and \(A = 47^{\circ}\), then \(BD=AB\sin A\).
\(BD = 18\sin47^{\circ}\approx18\times0.7314 = 13.1652\)

Step2: Find \(m\angle CDB\)

In right - triangle \(BCD\), \(\sin\angle CDB=\frac{BC}{BD}\). Given \(BC = 7\) and \(BD\approx13.1652\), then \(\sin\angle CDB=\frac{7}{13.1652}\approx0.5318\)
Using the inverse - sine function \(\angle CDB=\sin^{- 1}(0.5318)\approx32^{\circ}\)

Answer:

\(m\angle CDB\approx32^{\circ}\)